The Wikipedia article on Annulment discusses the topic in some detail, but does not answer this specific question. Since this is a legal process, whether secular or canonical, there are documents, and ultimately a decree voiding the marriage or a decree of nullity, thus there is documentation. I could envision that the file is sealed, but this point is not addressed either.
I have occasionally seen in old marriage registers where a record has been crossed out, but without explanation. Could these have been an annulment, or perhaps the marriage was not completed for another reason?